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Article Title: How responsive are real exchange rates in developing countries to terms of trade shocks? Corresponding author name: Lavan Mahadeva Address & telephone: International Finance Division, Bank of England, HO3, Threadneedle Street, London EC2R 8AH. Tel +442076013191

E-mail: lavanito@gmail.com

Other authors’ names: Juan Carlos Parra Alvarez Time schedule of manuscript submission:

Received: 17.05.10 Revised: 10.10.10 Accepted:

Publication Type: FLA

Full Length Article (FLA) Conference Paper (CFP) Economic Note (ECO)

Editorial Composition:

Number of Pages: 23 Number of Figures:1 Number of Tables:8

Editorial Office Note: Approved by: Date:

Dreve Lansrode, Rhode St. Genese, Belgium 1640 E-mail: Editor@EconModels.com

How responsive are real exchange rates in developing countries toterms of trade shocks?

Lavan Mahadeva1,∗, Juan Carlos Parra Alvarez2

Abstract

In developing countries, policy assessments about the reaction of the domestic economy to

external shocks depend on the degree of substitution between domestic and imported items. We

estimate these key parameters for Colombia. We find that the input of the distribution sector in

transforming imports is complementary, implying a great potential sensitivity of the Colombian

economy to external shocks. However we also find that consumption imports at the point of sale

are substitutes with domestic items. Even though the distribution sector is smaller, its influence

may dominate because the responsiveness of the real exchange rate is highly nonlinear in the

elasticity.

Keywords: Exchange Rate Policy, Elasticity, Colombia, Kalman Filter.JEL Classification: F47, E01, C61.

1. Introduction

In small open economies, the policy assessment of the impact external shocks depend cru-

cially on the degree of substitution between domestic and imported goods. We follow Devaragan

et al. (1990) in demonstrating that the response of the real exchange rate to a terms of trade

shock is sensitive to how complementary imports are to domestically produced items in consump-

IWe would like to thank Andrés González Gómez for his advice. The paper does not reflect the views of theBoard of Directors of the Banco de la República.

∗Corresponding author. Carrera 7 No. 14 - 78, Bogotá D.C., Colombia. Tel: +(571)3430895 Fax:+(571)2819735.

Email addresses: lavanito@gmail.com (Lavan Mahadeva), jparraal@banrep.gov.co (Juan Carlos ParraAlvarez)

1Adviser to the Governor. Banco de la República de Colombia.2Economist, Macroeconomic Modeling Department, Banco de la República de Colombia.

Preprint submitted to Elsevier February 9, 2011

tion. But McDaniel & Balistreri (2003) also document that many of the answers that general

equilibrium models traditionally provide to trade policy questions hinge on these elasticities,

traditionally called Armington elasticities after Armington (1969)’s seminal paper.

As developing countries have continued to open up to trade in goods and capital, there is an

ever greater interest on policy questions which depend on these elasticities. For instance Abrego

& Whalley (2000) demonstrate that these critical elasticities shape how trade openness affects

wage inequality. Yet another illustration concerns import price passthrough. As the domestic

output gap influences the final price of imported goods through imported domestically produced

margins of commerce on imported goods (Côté et al., 2006), the more complementary the role

of the distribution sector in the transport, marketing and sale of imported goods, the greater

the leverage of domestic conditions to dampen any persistent imported price rises. As a final

example, a recent paper shows that the elasticity of demand for nontradables and tradables

could critically determine the scale of the capital outflow and real exchange rate depreciation

during a financial crisis in a developing country with accumulated debt (Bianchi, 2009, pp.23).

Naturally then the models used to provide policy advice for small open economies split

production into aggregated tradable and nontradable sectors and put these elasticities on centre

stage. See for example, the open economy models described in Obstfeld & Rogoff (1996) or Galí

& Monacelli (2005)’s Dynamic Stochastic General Equilibrium model for open economies.

This paper estimates the substitutability between domestically produced and imported goods

in order to better assess the policy options of developing countries in the face of external shocks.

Taking Colombia to be a case study, we find that the input of the distribution sector is com-

plementary in transforming imports for final consumption. The value would suggest that the

real exchange rate can appreciate strongly in response to a positive terms of trade shock. Im-

ported investment goods are also complementary in combining with domestic investment goods.

But imported consumer goods are substitutes with domestic consumer goods and imported raw

materials also combine with consumer and investment imports with an elasticity not far above

the Cobb Douglas values. Both of these findings indicate that the real exchange rate would

respond little or may even depreciate. We show that the responsiveness of the real exchange

2

rate to a terms of trade shock is nonlinear, and so it may not be that the high consumption

elasticity offsets the low distribution sector elasticity. Our estimates allow for measurement

error in creating sectoral data as well as the possibility of a variety of trends that we find in the

the data, such as population growth, aggregate and sector-specific technological progress trends,

and changes in preferences or technology. Crucially, we also test if those estimates are robust.

Robustness is especially important because these parameters should be estimated at least at the

level of disaggregate sectors to avoid bias caused by aggregation which typically has the effect of

pushing estimates towards zero (Imbs & Mejean (2009)). But data on the disaggregate sectors

have to be purpose-built: National Accounts offices do not publish data on the real volumes

and deflators of these aggregate sectors. We find that the estimates of consumption elastici-

ties are very robust and of the distribution sector quite robust. The estimates of the imported

investment sensitivity are likely to be unreliable.

The paper is organized as follows. The theoretical foundation of these equations is explained

in the next section, Section 2. In Section 3 we describe how we adapt Colombian National

Accounts data to prepare a database for this model. Section 4 motivates our signal in broad

terms and then justifies its particular design. Results are reported for five individual demand

relationships in Section 5. Section 6 concludes.

2. Theory

2.1. Stylised illustration

A stylised model, adapted from Devaragan et al. (1990), can bring out the importance of

these elasticities for policy preoccupations. Let the demand for imported goods (Mt) as opposed

to domestically produced items (Dt) be described by the general function

Mt

Dt= f

(PmtPdt

)(1)

where Pmt and Pdt are the price of imports and domestically produced goods respectively.

Similarly the supply for export (Et) as opposed to that destined for domestic consumption is

3

given byEtDt

= g

(PetPdt

)(2)

where Pet is the domestic price of exports. The trade balance as a share of the value of GDP

(≡ PdtDt + PetEt) is defined as

BtPdtDt + PetEt

=

(PetPdt

EtDt− PmtPdt

Mt

Dt

)PdtDt

PdtDt + PetEt. (3)

The aim is to describe the effect of a terms of trade shock on the real exchange rate, assuming

that the trade balance as a share of GDP is constant. Substituting into equation 3 from equations

1 and 2 for Mt, Dt and Et, and differentiating and rearranging, yields

drertdtott

tottrert

=1− ω(

(1− ω)− DDtGDPt

PetEtPmtMt

(1− φ)) (4)

where the terms of trade is defined as tott ≡ PetPmt

, the real exchange rate is rert ≡ PetPdt

,

DDt ≡ PdtDt + PmtMt is domestic demand, φ is the elasticity of supply (equation 2)and ω is

the focus of this paper, the elasticity of demand between domestically produced and imported

goods from equation 3. If ω = 0, the two items are Leontieff complements, if ω = 1, they are

Cobb-Douglas complements, and if ω =∞, they are perfect substitutes.

In general, the elasticity of the real exchange rate to the terms of trade depends on the

the degree of substitution between domestic and imported goods with the trade balance held

to a fixed share of GDP. If the elasticity is unitary, the Cobb Douglas value, there will be no

response. Otherwise the response can vary in direction and scale. If exports and domestic

items are complements in production, as is likely, the relationship is monotonically increasing,

such that the more complementary are imported goods in demand, the greater the appreciation

we are likely to see from a positive terms of trade shock. But the relationship is also highly

nonlinear. Consider what would happen if it falls within the range:

1− DDt

GDPt

PetEtPmtMt

(1− φ) < ω < 1. (5)

4

5 is certainly possible. That ω lies above the lower bound is plausible because domestic demand

is not likely to be much greater than GDP, and exports not much greater than imports, while

the elasticity of export supply is likely to be smaller than the elasticity of demand for imports

relative to domestic goods. And as we shall see , we can find values of ω below the Cobb-Douglas

value of 1, keeping below the upper bound.

The point is that if ω lies in the range 5, a positive terms of trade shock will imply a real

appreciation (drertdtotttottrert

< 0), and with the denominator potentially small, that appreciation can

be large. The intuition is that when the terms of trade improve, there must be a rise in the share

of imports in domestic consumption to match the rise in the value of exports in production so

as to keep the trade balance fixed. If imports are complementary in consumption, but export

price elasticities are even lower, then the price of domestic items must rise to be consistent with

the greater share of spending on imports. That rise, above the domestic currency export price,

implies a real appreciation.

In summary, this simple model illustrates that policy assessment of international shocks

in open economies has to be based on an assessment of the elasticity of demand for domestic

goods. This would account for the fact that the production of goods and services sold for final

or intermediate consumption is vertically disintegrated across the national border and where

the distribution sector plays a potentially important role.

In the rest of this section, the key relationships that can be used to estimate these elasticities

are derived from theory. Although these relations can be couched in a general equilibrium

model,we do not do that here. In what follows, the convention is to denote per capita volumes

by lower case and aggregate volumes by upper case. Our specification and estimation strategy is

together general enough to allow for realistic features such as population growth and technical

progress and relative price trends. It is also worth noting that the relationship between the

real exchange rate terms of trade response and the elasticity of substitution of imports is highly

nonlinear, and therefore it may not be the case that the effect of an elasticity just below the

Cobb Douglas value in one sector is offset by a value of just above zero in another even more

important sector. As we shall see this might very well be the case with Colombia.

5

2.2. Distribution

We first describe the role of the transport and distribution sector (henceforth just the dis-

tribution sector) in taking imports of consumer and investment goods from outside the national

frontier, transporting them, storing them, marketing them and selling them to the consumer.

Imports at the dock are combined with the output of the domestic distribution with both then

taken as intermediate inputs that deliver the final consumption item. The price of the domestic

input is the margin. Burstein et al. (2003) found that in the case of Argentina, distribution

margins are more than 40% of the retail price of the average consumer good. They argue that

allowing for this, as one should, is critical to understanding the behaviour of the real exchange

rate during exchange-rate-based stabilizations.

In what follows Tt is the real domestic input of the distribution sector, Mdt is the volume of

imported consumption and investment goods at the point of use, and Mpt is the volume of these

goods at the docks, before transformation. PTt , Pmdt and Pmpt are the respective prices. The

transformation function is:

Mdt = zmt M (Tt,M

pt ) = zmt

[ι

1am

Tt (Tt)am−1am + (1− ιTt)

1am (Mp

t )am−1am

] amam−1

(6)

with am ≥ 0 is the elasticity of substitution between the domestically produced distribution

input and foreign imports, taking exactly the same range of values as in equation 4.

The maximisation problem of these firms is

max{Tt,Mp

t }Pmdt Md

t − PTt Tt − Pmpt Mp

t

s.t. Mdt ≤ zmt

[ι

1am

Tt (Tt)am−1am + (1− ιTt)

1am (Mp

t )am−1am

] amam−1

(7)

The solution to this problem yields the following relationship between the share parameters

in the Constant Elasticity of Substitution (CES) consumption function and the relative price

and nominal share of spending on domestically produced items, which will form the basis of our

6

estimate of the key parameter am:

PTt TtPmdt Md

t

= (zmt )am−1

(PTtPmdt

)1−amιTt. (8)

2.3. Consumption

In a similar fashion, a formal description of the representative consumer’s decision can yield

equations to estimate the elasticity of substitution between domestically produced and foreign

produced consumer goods. Total consumption can be described as a CES aggregate of the

consumption of domestically produced(cdt)and foreign produced items (cmt ),

ct = c(cdt , c

mt

)=

[γ

1ωt

(cdt)ω−1

ω + (1− γt)1ω (cmt )

ω−1ω

] ωω−1

. (9)

The solution to the problem of allocating consumption between foreign and domestically

produced items subject to a budget constraint is then expressed in share and relative price

terms:P cdt CDtP ct Ct

=

(P cdtP ct

)1−ω

γt, (10)

with P cdt and P ct being the respective prices of domestic items and of total consumption.

2.4. Investment

The substitutability of domestically produced investment goods, such as structures, with

foreign produced investment goods, such as machinery, also matters in determining the respon-

siveness of the economy to external shocks.

As an approximation, we assume that domestic producers create an aggregate investment

good by combining domestically produced investment, Xdt , with foreign produced investment,

Xmt ,:

Xt = zxtX(Xdt , X

mt

)= zxt

[(κt)

1ι(Xdt

) ι−1ι + (1− κt)

1ι (Xm

t )ι−1ι

] ιι−1

(11)

7

whereXt is aggregate gross investment. P xdt , Pmdt and P xt are the deflators of domestic, imported

and total investment goods respectively. The maximisation problem is:

max P xt Xt − P xdt Xdt − Pmt Xm

t

s.t. xt ≤ zxt[(κt)

1ι(Xdt

) ι−1ι + (1− κt)

1ι (Xm

t )ι−1ι

] ιι−1

. (12)

The solution implies the familiar share and relative price equation:

P xdt Xdt

P xt Xt= (zxt )

ι−1(P xdtP xt

)1−ι

κt. (13)

2.5. Raw material imports

It seems plausible that raw material imports require less transformation by the distribution

sector before consumption than imported capital and consumption goods. To test then if im-

ported raw materials are a complementary input into the economy, we estimate the elasticity

of raw materials relative to imports of consumer and investment goods in being disaggregated

from total imports.

Pumt is the total imports deflator from national accounts, that is, the price of imports be-

fore transformation by the distribution sector. Mut is the equivalent volume of imports at the

dock. The price of consumption and capital imports before transformation is Pmpt , the domestic

currency raw material price before transformation is P rmt and the volume of raw materials is

RMt.

The maximisation problem is then:

max{Mp

t , RMt}Pumt Mu

t − P rmt RMt − Pmpt Mpt

s.t. Mut ≤ zrmt

[(ιrmt)

1ar (RMt)

ar−1ar + (1− ιrmt)

1ar (Mp

t )ar−1ar

] amam−1

(14)

8

The solution impliesP rmt RMt

Pumt Mut

= ιrmt (zrmt )

ar−1(P rmtPumt

)1−ar. (15)

2.6. The private sector consumer

Our model melds private sector consumers with the government. But we might want estimate

a household-only consumption elasticity. Analogously to problem 9 and its solution 10, an

equation for private sector’s demand for domestically produced consumption is given as:

P cdpt CpDtP cpt Cpt

=

(P cdpt

P cpt

)1−ωp

γpt , (16)

with the price and volume of domestically produced consumption private sector written as P cdpt

and CcpDt, and the price and volume of total private consumption as P cpt and Ccpt .

3. The data

Consider now the data we would need to estimate these crucial elasticities using equations

8, 10, 13, 15 and 16. We can divide our data needs into two. Table 1 includes the National

Accounts expenditure aggregates, which are all available as published series as both nominal

and real values for Colombia.

Table 1: National accounts data for the modelVariable Explanation National Accounts available data

P ct , Ct, P c

t Ct Consumption of households and government Nominal, real volumes

P xt , Xt, P x

t Xt Gross fixed capital formation and changes in inventories Nominal, real volumes

Pumt , Mu

t , Pumt Mu

t Total imports before transformation Nominal, real volumes

P cpt Price of private sector consumption CPI data

P rmt , RMt, P rm

t RMt Raw materials Nominal, real volumes

A second table includes the variables for which there is no National Accounts counterpart.

9

Table 2: Missing data for the modelVariable Explanation

P cmt , Cmt , Pcmt Cmt Consumption by households and government of direct imports

P cdt , Cdt , Pcdt Cdt Consumption by households and government of domestic production

P cdpt , CpDt, Pcdpt CpDt Consumption by households of domestic production

Pmdt ,Mdt , P

mdt Md

t Aggregate capital and consumption imports after transformation

Pmpt ,Mpt , P

mpt Mp

t Aggregate capital and consumption imports before transformation

PTt , Tt, PTt Tt Distribution sector input into transforming consumption and capital imports

P xmt , Xmt , P

xmt Xm

t Imported physical investment

P xdt , Xdt , P

xdt Xd

t Domestically produced physical investment

A popular method is to categorise sectoral output as either being a tradable or a nontradable

sector. Most typically the goods producing sectors are classified as tradables and services as

nontradables. Then the real volume and deflators series can be calculated as aggregates of these

components. But we find this approach very problematic as many sectors contain both tradable

and nontradable elements. On these grounds, we adopted a more complex tactic.

As a first step, we used the input-output tables and other national accounts estimates about

the import intensity of each sector. Weighting by intensity and adding gave us annual nominal

shares for some of the missing series in 2, such as imported consumption or the distribution

sector input. We interpolated and extrapolated those shares to cover our whole sample at a

quarterly frequency. Aside from this, we obtained data on either the price and volume split of

other missing series from other parts of National Accounts data or from other sources. And we

already had data on aggregates both as prices and volume: the series in 1.

To complete the exercise, we had to produce series on what was left over, either a missing

component’s price or volume. The reason for this is that even if we have data for the series P1t,

Pt, Zt and P1tZ1t

PtZtin the formula

P1tZ1t + P2tZ2t = PtZt,

10

that would not be enough to derive the component P2t and Z2t separately.

There are two ways to overcome this impasse. We could either make use of strong assump-

tions about relative prices, for example that they are fixed (P1t = P2t), or we could employ index

number formulae. In the example above, an index formula could give Z2t as a value-added com-

ponent. Index number formulae are designed to be compatible with a wider range of utility

and production functions than the specific CES forms assumed in our derivations (Diewert &

Nakamura, 1993). And they do not require assumptions about particular values of elasticities,

as would the CES aggregate implied by our theoretical derivations.

We used index numbers as much as possible because they suited our purpose well. But we

still had to assume fixed relative prices between firms’ inventories and their investment; between

imported consumption and imported investment and in the government and private consumers’

purchase of domestically produced goods. Bold assumptions such as these are unavoidable

when building tradable nontradable sector models. At least our estimation strategy allowed us

to highlight the risks to our estimates if these assumptions is not supported by the data.

4. Estimation strategy

In this section we explain how we estimated the crucial elasticities and tested their reliability.

In a nutshell, each equation is estimated by regressing the nominal share of a nontradable

sector in the total on its relative price. Our estimates of the key elasticities of substitution

are based on the five pairs of equations that link relative price and shares across tradable and

non-tradable sectors: the input of the distribution sector in transforming capital and consumer

imports (equation 8); domestic consumption as a share of total consumption (equation 10);

domestic investment relative to total investment (equation 13); raw materials relative to total

imports (equation 15) and private sector domestic good consumption relative to total private

consumption (equation 16).

In the case of the demand for consumption of domestic production versus imported con-

sumption items, this equation can be written as:

11

scdt =

(P cdtP ct

)1−ω

γt (17)

where scdt is the nominal share of domestically produced consumption in total consumption.

These demand and supply relations are a suitable basis from which assess our model-database

combination. First as we are regressing a nominal share on a relative price, this relationship

should work well even if the data features population changes, aggregate or sectoral productivity

shifts. The relationship will only break down when there are problems in modelling these trends.

To see why, remember that in the case of domestic consumption, we did not use the the-

oretical price aggregator relationship to calculate the price index for domestically produced

consumption but instead a more general index number formula. Thus if P cdt refers to the the-

oretically consistent domestic good consumption deflator and P dat,cdt refers to our index, then

the share of domestic consumption is given by:

scdt =

(P cdtP ct

)1−ω

γt

⇒ scdt =

(P dat,cdt

P ct

)1−ω

γt

(P cdt

P dat,cdt

)1−ω

⇒ scdt =

(P dat,cdt

P ct

)1−ω

ϑt (18)

and so a composite residual term comprises the measurement error and the true parameter, γt,

ϑt ≡ γt

(P cdt

P dat,cdt

)1−ω

.

If there were any mismatch between our relative price indices and the true data generating

process, that would show up in the residual ϑt. This might happen if there were errors in our

construction of nontradable and tradable price series. One reason could be an important inter-

mediate trade between tradable and nontradable sectors which should in principle be modelled

12

(Valadkhani, 2004; Basu, 1995) but in practice is difficult to do. Another source of error could

also be a shift in the technical progress in the production of domestically produced items relative

to all other goods that is not captured in the data, especially where the quality of the goods are

improved. For example in the equation for investment goods (13) there could be a shift in the

term zxt .

ϑt may also include misspecifications in the model rather than the data. Another reason

for a residual would be that the imposed model may excessively restrict preferences, such as

imposing a constant γt when in reality this parameter shifts. For example the CES functional

form may be at odds with a reality that requires more general formulae3.

Our estimates are based on a state-space model of equation 18. We favour the state-space

format because it can incorporate the desired features that ϑt can be a time-varying unobserved

component and that the model includes some process for the relative price series.

We assume that ϑt follows the AR(1) state process:

ln (ϑt) = φ11 ln (ϑt−1) + u1t. (19)

Then the observation equation of the state-space model is:

yt= Hαt (20)

and the state equation is:

αt= Φαt−1+Ξ + ut (21)

with

αt≡ [ln (ϑt) , ln (xt)]T; (22)

yt ≡[

ln(P cdtP ct

) ln (scdt)

]T; (23)

3Fernández-Villaverde & Rubio-Ramírez (2007) present some other examples. Imbs & Mejean (2009) alsoestimate the same elasticities with very similar specifications, using similar arguments to ours.

13

ut ≡[u1t u2t

]T; (24)

Φ ≡

φ11 0

0 φ22

; (25)

Ξ ≡

(1− φ11) ξ1

(1− φ22) ξ2

; (26)

Q ≡

σ2u1 0

0 σ2u2

; (27)

and

H ≡

0 1

1 1− ω

. (28)

The observation equations are first a simple definition which links the state process for the

relative price to the data series and second, the share demand equation, equation 18, expressed

in log terms. The two state equations describe how ϑt and the relative price, xt, both in logs,

evolve. Thus the model allows for a time-varying ϑt and a time-varying share, and for the two

to be cointegrated jointly with the relative price. All unobserved stochastic variation in the

relationship is subsumed in ϑt, including any measurement error.

But even a simple state-space model such as this can involve some severe identification

problems. Using data on the relative price and the share only it is difficult to jointly identify

all the three constants and three variances. To overcome this we adopted a two-step approach.

We first estimate an AR(1) process for relative prices by ordinary least squares (OLS):

ln(P cdtP ct

) = ξ2 + φ22 ln(P cdt−1P ct−1

) + uOLS2t ,

and u2t ∼ N(0, σ2u2). (29)

The values of the parameter estimates for this process ξ2, φ22 and σ2u2 were imposed in a

14

second stage where we estimated the values for the remaining parameters (φ11, ξ1, σ2u1 and ω)

by maximum likelihood within the state-space model. The admissible values of parameters were

restricted as follows

φ11 ∈ [0, 1] , (30)

ω ∈ [0,∞] , (31)

σ2u1 ∈ [0,∞] , (32)

and

ξ1 ∈[0.01 + {ln (scdt)}12 − (1− ω) ∗

{ln(

P cdtP ct

)

}12

,−0.01 + {ln (scdt)}12 − (1− ω) ∗{ln(

P cdtP ct

)

}12

].

(33)

Restriction 30 ensures that this is a positive autocorrelated process. Restriction 31 keeps the

elasticity of demand to its permissible range. {ln (scdt)}12 and{ln(

P cdtP ct

)}12, are the mean values

of the last three years of the estimation sample only. Hence restriction 33 implies that the initial

value of the mean of ϑ would compensate for any systematic error in the recent residuals of the

share demand equation. This mechanical rule incorporate the typical practice of extrapolating

residuals to allow for possible structural breaks.

We estimated only the demand function for only one item in a two good system. The second

equation would be redundant under the null that the price aggregator is correct.

Even if we avoided using tight theoretical assumptions when we constructed our data, they

are still essentially purpose built. Hence we do not consider standard errors of the estimates

or in sample goodness of fit to be a good indication of the reliability of the estimates in giving

policy advice. And then, in practice, policy advice is predicated on models that accommodate

for residuals; often exogenous time series models will be used to extrapolate residuals into the

forecasts. Therefore what threatens policy advice is not the presence of a residual in the equation

from which we estimate the key parameter se, but whether or not that residual is difficult to

forecast. In this sense it matters not whether or not there is a large residual or even if it is

15

trending, but only whether or not it is predictable.

To incorporate these insights, we assess our models in predicting the nominal shares over the

last two years of quarterly data without using any of that data whatsoever in the estimation

sample. Neither do we use the last two years’ data on the relative prices; that series also has

to be forecasted also within the state-space model. We assess the model on the basis of the

Root Mean Squared Errors (RMSEs) in predicting the share series. In what follows, N is the

estimation sample size comprising 50 quarterly observations.

Our data is plotted in Figure 1. If the relative prices are rising, then a fall in share would

indicate the two components are complements and the estimate of the elasticity should pick this

up. Note also that the estimate is judged by its ability to forecast the data on nominal shares

to the right of the line. Immediately one can see that this is a serious challenge. Typically the

share data is characterised by irregular cycles. This makes the trade off between anticipating a

turning point or chasing the recent trend in the forecast period difficult.

5. Results

We can now turn to the parameter estimates, presented in Tables 3 to 7. The estimated

elasticities of substitution (here all described as ω) as well as the other parameters provide rich

information on Colombia’s susceptibility to external shocks.

Table 3: Distribution in consumption and investment importsMax. likelihood

est.φ11 0.13

100*σ11 5.21

100*exp(ξ1) 28.72

ω 0.77

To begin with the estimated elasticity for the distribution sector indicates complementarity

between domestic and imported items in the distribution transformation problem. The value

16

Figure 1: Data on five demand and supply relationships

of 0.77 could easily place it within the range of sensitivity identified in Section 2.1. And the

long-run share, exp(ξ1) capturing the average value of ιTt in equation 6, is estimated to be

about 30%, implying that distribution is an important input into the final sale of imported

consumption and investment goods.

On the other hand, we find that the elasticity of imports in consumption lies well above the

Cobb Douglas restriction of one, indicating that there is not a great deal of sensitivity to external

shocks for complementarity in arising from consumption. But as the effect of the elasticity on

the real exchange rate is nonlinear in values of these elasticities around the Cobb Douglas value,

the higher elasticity here might not offset of the influence of the distribution sector in exposing

vulnerability.

But foreign and domestic investment are judged to be very strong complements; the data

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Table 4: Domestic consumption of government and householdsMax. likelihood

est.φ11 0.23

100*σ11 0.93

100*exp(ξ1) 87.6

ω 1.69

Table 5: Domestic investmentMax. likelihood

est.φ11 0.02

100*σ11 9.24

100*exp(ξ1) 64.24

ω 0.20

would have the elasticity of substitution close to the permissible lower bound of Leontieoff. This

is some tentative evidence for a strong income effect associated with investment such that when

either domestic or foreign investment becomes cheap, spending on both rises.

Then raw material imports are found to be close to Cobb Douglas substitutes to to con-

sumption and investment items. In so far as imported raw materials require less domestic input

before being transformed, this does not magnify the complementarity we highlighted in the

distribution sector’s role in importing consumer and investment goods.

Comparing Table 4 and Table 7, it appears that households are less likely to substitute

domestic production for imports than the public sector. This might seem odd, bearing in mind

that the government employs a larger proportion of domestic value-added factors of production

than a typical tradable sector would do. But the governments consumption is different from

its use of labour and capital inputs. In Colombia it is plausible that the government imports

a large share of its consumption, for example, in defence. In any case, as a result, the private

sector consumption elasticity is found to be close to the Cobb Douglas value.

In all cases the standard deviation of the unobserved component lie above zero. Thus the

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Table 6: Raw materials in importsMax. likelihood

est.φ11 0.03

100*σ11 4.55

100*exp(ξ1) 44.38

ω 1.23

Table 7: Domestic consumption of householdsMax. likelihood

est.φ11 0.23

100*σ11 1.09

100*exp(ξ1) 82.24

ω 1.29

data favour time variation in ϑ over a fixed coefficient and vindicate our state space method.

The estimated distributions of the parameter φ11 in each model are also revealing. In the case

of investment especially this value is quite low meaning that there is very little information from

past values that the Kalman Filter can use to build a forecast investment; the series is both

volatile and not persistent.

The robustness of these estimates is tested by reporting on the forecast performance of

the whole system. Table 8 reports the RMSEs from all five individual demand and supply

relationships.

At first glance, the RMSEs in Table 8 all seem large. But these are forecasts made with our

simple model. We would argue that the lowest RMSE here are consistent with what could be

satisfactory performance when combined with off model judgement.

The RMSE in predicting distribution output share in the transformation of non raw material

imports is larger at 8.2%. Given all the assumptions we had to employ to get this data, this is

quite reassuring. We note however that the bootstrapped mean turned out to be much higher

than the bootstrapped mode, indicating that there is a risk of some large errors.

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Table 8: Estimates of the five demand relationshipsRMSE estimates, calculated from the state-space.

Max. likelihoodest.

Distribution in consumption and investment imports 8.20 (4.19)

Domestic consumption of hhds and gvt 1.07 (1.33)

Domestic investment 9.76 (21.41)

Raw materials in imports 5.28 (9.05)

Domestic consumption of households 1.87 (1.67)

* average over year one of the forecast (average over year two in brackets).

The low RMSE for consumption of about 1.07% indicates little risk of forecast error origi-

nating in the relations in the demand for domestically produced consumption for government

and households together. While there is slightly more forecast error in the consumption problem

just for households, the size of the error remains low enough not to cause alarm there either.

The greater error might indicate either that the difference between the consumption deflator

and the consumer price index brings with it some cost, or that our assumption that the price

of domestic consumption is the same for government and for households.

But the greatest error by far is in the disaggregation of investment into its domestically

produced and foreign produced components. The RMSE is 9.76% for the first year and then

21.41% by the second. Clearly the model is missing some of the cyclical behaviour in investment.

This could be because Colombian investment data is exceptionally volatile: the standard

deviation of a detrended real investment series (including changes in inventories) is 18% com-

pared to 8% for the same concept in UK data (both calculated on annual data from 1970-2007).

This may be due to poor fixed investment data; it may be because there are irregular cycles in

inventories; it may be because inventories are where the National Accounts office allocates its

residual; it may also be due to aspects of tastes and technology not incorporated in our func-

tion form. For example the homothetic CES functional form may be restricting our investment

model excessively.

Finally , we also note that the separation of raw materials from total imports does not involve

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too much unpredictability: the RMSE here is 5.28% for one year ahead.

6. Conclusions

Key policy decisions in open economies depend on values of parameters which capture the

substitutability between tradable and nontradable sectors. We derived five important equations

that straddle this split and compiled the data needed to estimate them for Colombia. A common

feature of all equations, was that importing sectors were separated from domestic production,

and for this reason, the database had to be purpose-built.

We estimated these equations. Our method takes account of prosaic adaptations that are

made in using these parameters to give policy advice. Rather than using the theory of the

model to derive data on the relative price series, we used more general index numbers. As these

index numbers include the theoretical equations of the model as a special case, a residual would

then appear in these key equations when the model and data were inconsistent. If that residual

cannot be forecasted, it is likely that policy prescriptions based on these estimates would also

prove unreliable.

Our estimates revealed that the contribution of the distribution sector in bringing imports to

final consumers in Colombia is quite complementary to imports at the dock, with the estimates

of the elasticity falling within the range of values that would imply that positive terms of

trade shocks lead to large appreciations. Consumption imports appear to weak substitutes with

domestic goods, favouring the opposite reaction. Both these estimates seemed to be relatively

reliable. Given that the relation between these elasticities and the real exchange rate response is

nonlinear, it might very well be that the distribution sector elasticity drives the overall response.

Estimates of imported investment indicated that it was a very strong complement with

domestic investment in creating the capital stock of Colombia. But these estimates were also

shown to be least reliable.

We can speculate as to how these important elasticities could evolve in the future. Broda &

Weinstein (2006) observed that globalisation of the form of a greater vertical disintegration of

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production across national borders has lowered these elasticities for the United States. If this

also holds true for developing countries, one might expect greater appreciations following terms

of trade shocks in the future. On the other hand, improvements in the infrastructure (Colombia

has a notoriously difficult terrain for importers) may act against this, by lowering importers’

margins and raising the degree of substitutability. Our estimates suggest that monitoring these

developments will be crucial in policy assessments of the responsiveness of the domestic economy

to external shocks.

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